# rand

## Pseudo random number generation

Random number generator.

The module contains several different algorithms and can be extended with more in the future. The current uniform distribution algorithms uses the scrambled Xorshift algorithms by Sebastiano Vigna and the normal distribution algorithm uses the Ziggurat Method by Marsaglia and Tsang.

The implemented algorithms are:

`exsplus`
Xorshift116+, 58 bits precision and period of 2^116-1.
`exs64`
Xorshift64*, 64 bits precision and a period of 2^64-1.
`exs1024`
Xorshift1024*, 64 bits precision and a period of 2^1024-1.

The current default algorithm is `exsplus`. The default may change in future. If a specific algorithm is required make sure to always use seed/1 to initialize the state.

Every time a random number is requested, a state is used to calculate it and a new state produced. The state can either be implicit or it can be an explicit argument and return value.

The functions with implicit state use the process dictionary variable `rand_seed` to remember the current state.

If a process calls uniform/0 or uniform/1 without setting a seed first, seed/1 is called automatically with the default algorithm and creates a non-constant seed.

The functions with explicit state never use the process dictionary.

Examples:

```      %% Simple usage. Creates and seeds the default algorithm
%% with a non-constant seed if not already done.
R0 = rand:uniform(),
R1 = rand:uniform(),

%% Use a given algorithm.
_ = rand:seed(exs1024),
R2 = rand:uniform(),

%% Use a given algorithm with a constant seed.
_ = rand:seed(exs1024, {123, 123534, 345345}),
R3 = rand:uniform(),

%% Use the functional api with non-constant seed.
S0 = rand:seed_s(exsplus),
{R4, S1} = rand:uniform_s(S0),

%% Create a standard normal deviate.
{SND0, S2} = rand:normal_s(S1),
```

## Note!

This random number generator is not cryptographically strong. If a strong cryptographic random number generator is needed, use one of functions in the crypto module, for example `crypto:strong_rand_bytes/1`.

### state()

Algorithm dependent state.

### export_state()

Algorithm dependent state which can be printed or saved to file.

### seed(AlgOrExpState :: alg() | export_state()) -> state()

Seeds random number generation with the given algorithm and time dependent data if AlgOrExpState is an algorithm.

Otherwise recreates the exported seed in the process dictionary, and returns the state. See also: export_seed/0.

### seed_s(AlgOrExpState :: alg() | export_state()) -> state()

Seeds random number generation with the given algorithm and time dependent data if AlgOrExpState is an algorithm.

Otherwise recreates the exported seed and returns the state. See also: export_seed/0.

### seed(Alg :: alg(), S0 :: {integer(), integer(), integer()}) ->state()

Seeds random number generation with the given algorithm and integers in the process dictionary and returns the state.

### seed_s(Alg :: alg(), S0 :: {integer(), integer(), integer()}) ->state()

Seeds random number generation with the given algorithm and integers and returns the state.

### export_seed() -> undefined | export_state()

Returns the random number state in an external format. To be used with seed/1.

### export_seed_s(X1 :: state()) -> export_state()

Returns the random number generator state in an external format. To be used with seed/1.

### uniform() -> X :: float()

Returns a random float uniformly distributed in the value range `0.0 < X < 1.0 ` and updates the state in the process dictionary.

### uniform_s(State :: state()) -> {X :: float(), NewS :: state()}

Given a state, `uniform_s/1` returns a random float uniformly distributed in the value range ```0.0 < X < 1.0``` and a new state.

### uniform(N :: integer() >= 1) -> X :: integer() >= 1

Given an integer `N >= 1`, `uniform/1` returns a random integer uniformly distributed in the value range `1 <= X <= N` and updates the state in the process dictionary.

### uniform_s(N :: integer() >= 1, State :: state()) ->              {X :: integer() >= 1, NewS :: state()}

Given an integer `N >= 1` and a state, `uniform_s/2` returns a random integer uniformly distributed in the value range ```1 <= X <= N``` and a new state.

### normal() -> float()

Returns a standard normal deviate float (that is, the mean is 0 and the standard deviation is 1) and updates the state in the process dictionary.

### normal_s(State0 :: state()) -> {float(), NewS :: state()}

Given a state, `normal_s/1` returns a standard normal deviate float (that is, the mean is 0 and the standard deviation is 1) and a new state.